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arxiv: 1009.4407 · v3 · pith:L4JGK5QMnew · submitted 2010-09-22 · 🧮 math.MG · cs.NA· math.CO· math.NA

Optimal asymptotic bounds for spherical designs

Andriy Bondarenko , Danylo Radchenko , Maryna Viazovska This is my paper
classification 🧮 math.MG cs.NAmath.COmath.NA
keywords sphericalasymptoticboundsconjectureconsistingconstantdependingdesign
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In this paper we prove the conjecture of Korevaar and Meyers: for each $N\ge c_dt^d$ there exists a spherical $t$-design in the sphere $S^d$ consisting of $N$ points, where $c_d$ is a constant depending only on $d$.

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Cited by 2 Pith papers

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  1. The most discriminable quantum states in the multicopy regime

    quant-ph 2026-04 unverdicted novelty 7.0

    k-designs achieve maximal discriminability for pure states in multi-copy minimum-error discrimination; mixed states outperform for larger ensembles, with quantum offering quadratic advantage over classical.

  2. The most discriminable quantum states in the multicopy regime

    quant-ph 2026-04 unverdicted novelty 7.0

    k-designs achieve maximal multi-copy discriminability for pure states when N suffices, mixed states outperform beyond that, and quantum offers quadratic advantage over classical in Bayes capacity terms.